Do you all forget the web pre chrome? Google and Chrome forced browser vendors to do better by standards in the first place. Google’s stewardship forced browser vendors to compete like never before.
I don't remember Google doing that. What I remember from that time is a browser war happening between the power players in mobile with iOS, Android and Windows Phone.
I would attribute the improvement in browser standards support to the finalization of the HTML5 spec by the W3C in 2009, which led to browser vendors harmonizing their feature set. We still needed jQuery to ensure cross-browser support, and floats and polyfills to get sites to work on mobile. That ended when browsers harmonized ES2015 support and built in support for flexbox and grid.